Distance Calculations of a Football Field

80. To go to a football stadium from your house, you first drive 1000 m north, then 500 m west, and finally 1500 m south. (a) Relative to your home, the football stadium is (1) north of west, (2) south of east, (3) north of east, or (4) south of west.

(b) What is the straight-line distance from your house to the stadium?

88. Express the following calculations to the proper number of significant figures: (a) 12.634 + 2.1; (b) 13.5 - 2.134; (c) pie (0.25m) squared; (d) square root of 2.37/3.5

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80. To go to a football stadium from your house, you first drive 1000 m north, then 500 m west, and finally 1500 m south. (a) Relative to your home, the football stadium is (1) north of west, (2) south of east, (3) north of east, or (4) south of west.

(b) What is the straight-line distance from your house to the stadium?

88. Express the following calculations to the proper number of significant figures: (a) 12.634 + 2.1; (b) 13.5 - 2.134; (c) pie (0.25m) squared; (d) square root of 2.37/3.5

94. The radius of a solid sphere is 12 cm. What is the surface area of the sphere in

(a) square centimeters?

(b) square meters?

(c) If the mass of the sphere is 9.0 kg, what is the sphere's density in kilograms per cubic meter?

98. The average density of the Moon is 3.36g/cm cubed, and the Moon's diameter is 2160 mi. What is the total mass of the Moon in kilograms?

100. An airplane flies 100 mi south from city A to city B, 200 mi east from city B to city C, and then 300 mi north from city C to city D. (a) What is the straight-line distance from city A to city D? (b) What is the direction of city D relative to city A?

28. Two runners approaching each other on a straight track have constant speeds of 4.50 m / s and 3.50 m / s, respectively, when they are 100 m apart. How long will it take for the runners to meet, and at what position will they meet if they maintain these speeds?

40. A couple is traveling by car 40 km / h down a straight highway. They see an accident in the distance, so the driver applies the brakes, and in 5.0 s the car slows down uniformly to rest.

(a) The direction of the acceleration vector is (1) in the same direction as, (2) opposite to, OR (3) at 90 degrees relative to the velocity vector. Why?

(b) By how much must the velocity change each second from the start of braking to the car's complete stop?

88. An arrow is shot vertically upward. Three seconds later, it is at a height of 35 m. (a) What was the initial speed of the arrow? (b) How long is the arrow in flight from launch to returning to the initial height? (Assume the arrow falls vertically downward.)

68. Swimming at 0.15 m/s relative to still water, a swimmer heads directly across as 100-m-wide river. He arrives 50 m downstream from a point directly across the river from his starting point. (a) What is the speed of the current in the river? (b) In what direction should the swimmer head so as to arrive at a point directly opposite his starting point?

84. A soccer player kicks a stationary ball, giving it a speed of 20.0 m/s at an angle of 15.0 degrees to the horizontal.

(a) What is the maximum height reached by the ball?

(b) What is the ball's range?

(c) How could the range be increased?